有限元网格形状要尽可能规则,网格之间必须通过结点连接,这些要求给复杂形状求解域的数值计算带来很大的前处理工作负担,而且实际的曲线边界一般要离散成有限单元能够描述的形式,难以模拟CAD模型的精确几何。针对这些问题,基于独立覆盖流形法提出任意形状且任意连接的覆盖网格,在CAE分析中模拟CAD模型的精确几何边界及其边界条件:将求解域划分为可包含曲线边的任意形状的块体网格,可以采用单纯形解析积分和数值积分2种方式进行块体积分;仅需在积分过程中考虑块体之间的窄条形(包括曲线条)的覆盖重叠区域,而不必在计算模型中生成这些条形;通过边界条实现本质边界条件的严格施加,包括曲线上的边界条件;给出2个数值算例验证了方法的有效性。任意形状的覆盖网格将为实现基于精确几何模型的数值计算及其完全自动化的前处理开辟新的路径。

Finite element meshes should keep regular shape as much as possible, and ensure correct connections through nodes. These requirements pose a great burden to the pre-processing procedure of numerical computations for solving domains with complex shapes. On the other hand, curve boundaries in practical situations are usually discretized into shapes which finite element meshes can describe, resulting in an imprecise simulation of exact geometry defined in CAD. In view of this, cover meshes with arbitrary shapes and arbitrary connections are implemented using Manifold Method based on independent covers. Exact geometric boundaries of CAD models and boundary conditions are simulated in CAE analyses. The solving domain is divided into block meshes with arbitrary shapes which can contain curve boundaries. And two approaches, including analytical integration method with simplexes and numerical integration method, can be used for the block integration. The thin strips for cover overlapping are considered only in the integration process, but are not necessarily involved in the generation of computation models. Essential boundary conditions are strictly applied through boundary strips, including the boundary conditions on curves. Moreover, two numerical examples are given to illustrate the validity of the method. Cover meshes with arbitrary shapes bring about a new path for numerical computations based on exact geometric models and automatic pre-processing procedures.